Open-circuit fault-tolerant current setting method for five-phase permanent magnet motor considering the third harmonic of back-EMF

Abstract

The invention discloses a method for setting the fault-tolerant current of a five-phase permanent magnet motor under an open circuit fault considering the third harmonic of the back electromotive force, which belongs to the field of multi-phase permanent magnet motors. The invention improves the torque performance of a five-phase permanent magnet motor whose back electromotive force includes the third harmonic under an open circuit fault, so that the motor has the ability to operate smoothly under an open circuit fault. The method of the invention only adjusts the current phase of the non-open circuit phase when an open circuit fault occurs, suppresses the 2nd and 4th torque fluctuation components related to the back electromotive force fundamental wave and the third harmonic in the torque neutralization after the fault, so as to maintain the low torque fluctuation characteristics, and then realize stable fault-tolerant operation. The open circuit fault is divided into three types: one-phase winding open circuit fault, adjacent two-phase winding open circuit fault and relative two-phase winding open circuit fault. The limiting condition is that the zero-sequence current is not constrained. Under the premise of ensuring the torque output capacity of the motor, the invention effectively reduces the torque fluctuation of the fault-tolerant operation of the five-phase motor when a one-phase winding open circuit fault, an adjacent two-phase winding open circuit fault and a relative two-phase winding open circuit fault occur.

Description

Technical Field

[0001] The invention belongs to the field of multi-phase permanent magnet motors and relates to a fault-tolerant control technology under an open circuit fault. Background Art

[0002] Permanent magnet synchronous motors are widely used in modern vehicles, aerospace, high-end industrial equipment and other fields due to their significant advantages in efficiency and power density. Currently, three-phase permanent magnet synchronous motors are widely used, and their related supporting technologies are already very mature. However, the fault tolerance of traditional three-phase permanent magnet synchronous motors is poor, especially when the winding is open-circuited or short-circuited, the output torque characteristics of the motor deteriorate, or even fail to work, making it difficult to meet the stringent requirements of pure electric vehicles, aerospace, etc. for motor system reliability and fault tolerance. The phase redundancy characteristics of multi-phase permanent magnet motors give them better fault tolerance than traditional three-phase permanent magnet motors, and can meet the future development of pure electric vehicles and other fields for motor system reliability and fault tolerance.

[0003] Winding open circuit fault is a typical fault type in permanent magnet motors. When a winding open circuit fault occurs, the symmetry of the working winding in the motor is destroyed, and the magnetic field generated by the winding is no longer a circular rotating magnetic field, which makes the torque characteristics of the motor deteriorate, which is typically manifested as a decrease in the average torque and an increase in torque fluctuation. In order to enable the multi-phase permanent magnet motor to work reliably under a winding open circuit fault, it is necessary to develop a corresponding open circuit fault fault-tolerant control strategy to improve its torque output characteristics under the fault. The back electromotive force of a five-phase permanent magnet motor usually contains the third harmonic, which will bring additional torque fluctuation components under a winding open circuit fault. When formulating a winding open circuit fault fault-tolerant control strategy, by considering the influence of the third harmonic in the back electromotive force, it is beneficial to improve the control effect of the open circuit fault fault-tolerant control strategy and improve the torque output characteristics of the multi-phase permanent magnet motor under a winding open circuit fault. Summary of the invention

[0004] The purpose of the present invention is to improve the torque output characteristics of a five-phase permanent magnet motor under an open-circuit fault of a winding, and to provide a method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor taking into account the third harmonic of the back-EMF.

[0005] The method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor considering the third harmonic of back electromotive force of the present invention includes three schemes.

[0006] The first solution is applicable to the case where an open circuit fault occurs in any phase winding of a five-phase permanent magnet motor.

[0007] Taking the A-phase winding open circuit as an example, the fault-tolerant control method of the five-phase permanent magnet motor when any one-phase winding is open circuit is as follows:

[0008] Adjust the input current of the remaining four-phase windings B, C, D, and E according to

[0009]

[0010] Work is performed to improve post-fault torque characteristics;

[0011] In the formula, i B1 、i C1 、i D1 、i E1 are the adjusted B, C, D, and E phase winding currents, I m1 is the amplitude of the B, C, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 2 ,θ 3 ,θ 4 are the phases of the B, C, D, and E phase winding currents after adjustment respectively;

[0012] By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 1 ,θ 2 ,θ 3 ,θ 4 :

[0013]

[0014] In the formula, E 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0015] λ 1 and λ 2 is the Lagrangian operator, θ j The phases of the phase windings after adjustment are j=1, 2, 3, 4, corresponding to θ 1 ,θ 2 ,θ 3 ,θ 4 .

[0016] Preferably, obtain θ 1 ,θ 2 ,θ 3 ,θ 4 The process is:

[0017] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back electromotive force of the four-phase windings B, C, D, and E is:

[0018]

[0019] In the formula, e B 、e C 、e D and e Eare the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 and E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively;

[0020] When an open-circuit fault occurs in the A-phase winding, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0021]

[0022] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 、T 2 and T 4 They are the average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor respectively;

[0023] In order to improve the torque output characteristics of the five-phase permanent magnet motor after a one-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, while constraining the secondary fluctuation torque term to zero. The corresponding constraint condition expression is:

[0024]

[0025] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0026]

[0027] Then, the phase of the adjusted B, C, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 2 ,θ 3 ,θ 4 .

[0028] The second solution is applicable to the case where two adjacent phase windings of a five-phase permanent magnet motor have open circuit faults.

[0029] Taking the A and B phase windings as an example, the fault-tolerant control method of the five-phase permanent magnet motor when the adjacent two phase windings are open is as follows:

[0030] Adjust the remaining C, D, E three-phase winding input current according to

[0031]

[0032] Work is performed to improve post-fault torque characteristics;

[0033] In the formula, i C1 、i D1 、i E1 are the adjusted C, D, and E phase winding currents, Im1 is the amplitude of the C, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 2 ,θ 3 ,θ 4 are the phases of the adjusted C, D, and E phase winding currents respectively;

[0034] By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 2 ,θ 3 ,θ 4 :

[0035]

[0036] In the formula, E 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0037] λ 1 and λ 2 is the Lagrangian operator, θ j The phases of the phase winding current after adjustment j = 2, 3, 4, corresponding to θ 2 ,θ 3 ,θ 4 .

[0038] Preferably, obtain θ 2 ,θ 3 ,θ 4 The process is:

[0039] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the C, D, and E three-phase windings is:

[0040]

[0041] In the formula, e C 、e D and e E are the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 、E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively;

[0042] When an open circuit fault occurs in the A and B phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0043]

[0044] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4They are the average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor respectively;

[0045] In order to improve the torque output characteristics of the five-phase permanent magnet motor after the adjacent two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, and at the same time constrain the secondary fluctuation torque term to zero. The corresponding constraint condition expression is:

[0046]

[0047] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0048]

[0049] Then, the phase of the adjusted C, D, and E phase winding currents can be obtained, that is, θ 2 ,θ 3 ,θ 4 .

[0050] The third solution is applicable to the case where two-phase windings of a five-phase permanent magnet motor each have open circuit faults.

[0051] Taking the A and C phase windings as an example, the fault-tolerant control method of the five-phase permanent magnet motor when the two phase windings are open is as follows:

[0052] Adjust the remaining B, D, E three-phase winding input current according to

[0053]

[0054] Work is performed to improve post-fault torque characteristics;

[0055] In the formula, i B1 、i D1 、i E1 are the adjusted B, D, and E phase winding currents, I m1 is the amplitude of the B, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 3 ,θ 4 are the phases of the adjusted B, D, and E phase winding currents respectively;

[0056] By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 1 ,θ 3 ,θ 4 :

[0057]

[0058] In the formula, E 1and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0059] λ 1 and λ 2 is the Lagrangian operator, θ j is the adjusted phase winding current phase j = 1, 3, 4, corresponding to θ 1 ,θ 3 ,θ 4 .

[0060] Preferably, obtain θ 1 ,θ 3 ,θ 4 The process is:

[0061] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the three-phase windings B, D, and E is:

[0062]

[0063] In the formula, e B 、e D and e E are the no-load back EMF of the three-phase windings B, D, and E, respectively. 1 and E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively;

[0064] When an open circuit fault occurs in the A and C phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0065]

[0066] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 、T 2 and T 4 They are the average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor respectively;

[0067] In order to improve the torque output characteristics of the five-phase permanent magnet motor after a two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, while constraining the secondary fluctuation torque term to zero. The corresponding constraint condition expression is:

[0068]

[0069] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0070]

[0071] Then, the phase of the adjusted B, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 3 ,θ 4 .

[0072] Preferably, the five-phase permanent magnet motor is powered by a five-phase full-bridge inverter, a five-phase six-bridge-arm inverter or other five-phase multi-bridge-arm inverter that allows the neutral point current to be non-zero.

[0073] Beneficial effects of the invention: The invention discloses a method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor taking into account the third harmonic of the back electromotive force. When an open-circuit fault occurs in one phase, two adjacent phases, or two phases apart of the winding of the five-phase permanent magnet motor, the five-phase permanent magnet motor can output a relatively large torque after the fault while ensuring that the torque fluctuation is small. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a schematic diagram of the five-phase full-bridge inverter topology;

[0075] Figure 2 It is a schematic diagram of the topology of a five-phase six-bridge-arm inverter;

[0076] Figure 3 It is a schematic diagram of closing other switch tubes in the same bridge arm to form a winding open circuit fault when a switch tube open circuit fault occurs in a five-phase full-bridge inverter. DETAILED DESCRIPTION

[0077] The following will describe the implementation methods of the present invention in detail with reference to the accompanying drawings and embodiments, so that the implementation process of how the present invention applies technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly. It should be noted that as long as there is no conflict, the various embodiments of the present invention and the various features in the embodiments can be combined with each other, and the technical solutions formed are all within the protection scope of the present invention.

[0078] The method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor considering the third harmonic of the back-electromotive force described in this embodiment includes the situations where an open-circuit fault occurs in one-phase, two adjacent phases, and two-phase windings apart.

[0079] Specific implementation method 1: The following is combined Figures 1 to 3 This embodiment will be described.

[0080] Taking the A-phase winding open circuit as an example, the calculation method of the fault-tolerant current of the remaining normal windings of the five-phase permanent magnet motor when any phase winding is open circuit is as follows:

[0081] When an open-circuit fault occurs in the A-phase winding, the set values ​​of the input currents of the remaining B, C, D, and E four-phase windings are adjusted. The corresponding expression is:

[0082]

[0083] In the formula, i B1 、i C1 、i D1 、i E1 are the adjusted B, C, D, and E phase winding currents, I m1 is the amplitude of the B, C, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 2 ,θ 3 ,θ 4 are the phases of the B, C, D, and E phase winding currents after adjustment respectively;

[0084] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back electromotive force of the four-phase windings B, C, D, and E is:

[0085]

[0086] In the formula, e B 、e C 、e D and e E are the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0087] When an open-circuit fault occurs in the A-phase winding, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0088]

[0089] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 、T 2 and T 4 They are the average torque term, the second-order ripple torque term, and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor. It can be seen that in the case of an open-circuit fault in the winding, the third harmonic in the winding back electromotive force will introduce second-order and fourth-order torque fluctuations in the electromagnetic torque;

[0090] In order to improve the torque output characteristics of the five-phase permanent magnet motor after a one-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, and at the same time constrain the main component of the fluctuating torque, that is, the secondary fluctuating torque term, to zero. The corresponding constraint condition expression is:

[0091]

[0092] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0093]

[0094] In the formula, λ 1 , 2 is the Lagrangian operator;

[0095] Then, the phase of the adjusted B, C, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 2 ,θ 3 ,θ 4 .

[0096] Embodiment: A specific embodiment of a five-phase permanent magnet motor with an open-circuit fault in one phase winding is given below.

[0097] Taking a 15-slot 12-pole five-phase permanent magnet motor as an example, the output torque characteristics of the five-phase permanent magnet motor in a normal state, a one-phase winding open-circuit state, and after adopting the method of the present invention are given respectively, as shown in Table 1, to further illustrate the advantages of the method of the present invention.

[0098] Table 1 Comparison of torque characteristics under normal state and phase A open circuit fault state

[0099] Working status Normal state Phase A open circuit (not controlled) Phase A open circuit (fault-tolerant control) Output torque (N·m) 38 30.4 29.8 Torque ripple (%) 0.4 21.4 5

[0100] It can be seen that the open-circuit fault-tolerant current setting method of the five-phase permanent magnet motor considering the third harmonic of the back-electromotive force described in the present invention can significantly reduce the torque fluctuation of the five-phase permanent magnet motor under the open-circuit fault of one-phase winding, thereby better meeting the system application requirements. Specific implementation method 2:

[0102] Taking the A and B phase windings as an example, when two adjacent phase windings of a five-phase permanent magnet motor are open-circuited, the calculation method of the fault-tolerant current of the remaining normal windings is as follows:

[0103] When an open circuit fault occurs in the A and B phase windings, the set values ​​of the input currents of the remaining C, D, and E three-phase windings are adjusted. The corresponding expression is:

[0104]

[0105] In the formula, i C1 、i D1 、i E1 are the adjusted C, D, and E phase winding currents, I m1 is the amplitude of the C, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 2 ,θ 3 ,θ 4 are the phases of the adjusted C, D, and E phase winding currents respectively;

[0106] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the C, D, and E three-phase windings is:

[0107]

[0108] In the formula, e C 、e D and e E are the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0109] When an open circuit fault occurs in the A and B phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0110]

[0111] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4 They are the average torque term, the second-order ripple torque term, and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor. It can be seen that in the case of an open-circuit fault in the winding, the third harmonic in the winding back electromotive force will introduce second-order and fourth-order torque fluctuations in the electromagnetic torque;

[0112] In order to improve the torque output characteristics of the five-phase permanent magnet motor after the adjacent two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, and at the same time constrain the main component of the fluctuating torque, that is, the secondary fluctuating torque term, to zero. The corresponding constraint condition expression is:

[0113]

[0114] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0115]

[0116] In the formula, λ 1 , 2 is the Lagrangian operator;

[0117] Then, the phase of the adjusted C, D, and E phase winding currents can be obtained, that is, θ 2 ,θ 3 ,θ 4 . Specific implementation method three:

[0119] Taking the A and C phase windings as an example, when the two phase windings of the five-phase permanent magnet motor are open-circuited, the calculation method of the fault-tolerant current of the remaining normal windings is as follows:

[0120] When an open circuit fault occurs in the A and C phase windings, the set values ​​of the input currents of the remaining B, D, and E three-phase windings are adjusted. The corresponding expression is:

[0121]

[0122] In the formula, i B1 、i D1 、i E1 are the adjusted B, D, and E phase winding currents, I m1 is the amplitude of the B, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 3 ,θ 4 are the phases of the adjusted B, D, and E phase winding currents respectively;

[0123] When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the three-phase windings B, D, and E is:

[0124]

[0125] In the formula, e B 、e D and e E are the no-load back EMF of the three-phase windings B, D, and E, respectively. 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively;

[0126] When an open circuit fault occurs in the A and C phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is:

[0127]

[0128] Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4 They are the average torque term, the second-order ripple torque term, and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor. It can be seen that in the case of an open-circuit fault in the winding, the third harmonic in the winding back electromotive force will introduce second-order and fourth-order torque fluctuations in the electromagnetic torque;

[0129] In order to improve the torque output characteristics of the five-phase permanent magnet motor after a two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, and at the same time constrain the main component of the fluctuating torque, that is, the secondary fluctuating torque term, to zero. The corresponding constraint condition expression is:

[0130]

[0131] Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows:

[0132]

[0133] In the formula, λ 1 , 2 is the Lagrangian operator;

[0134] Then, the phase of the adjusted B, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 3 ,θ 4 .

[0135] Although the embodiments disclosed in the present invention are as above, the above contents are only embodiments adopted for facilitating the understanding of the present invention and are not intended to limit the present invention. Any technician in the technical field to which the present invention belongs can make any modifications and changes in the form and details of the implementation without departing from the spirit and scope disclosed in the present invention, but the patent protection scope of the present invention shall still be subject to the scope defined in the attached claims.

Claims

1. Open-circuit fault-tolerant current setting method for five-phase permanent magnet motor considering the third harmonic of back EMF, It is characterized in that The method includes a fault-tolerant control method for an open circuit of the A-phase winding: When the A phase winding is open circuit, adjust the input current of the remaining B, C, D, and E phase windings according to Work is performed to improve post-fault torque characteristics; In the formula, i B1 、i C1 、i D1 、i E1 are the adjusted B, C, D, and E phase winding currents, I m1 is the amplitude of the B, C, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 2 ,θ 3 ,θ 4 are the phases of the B, C, D, and E phase winding currents after adjustment respectively; By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 1 ,θ 2 ,θ 3 ,θ 4 : In the formula, E 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively; λ 1 and λ 2 is the Lagrangian operator, θ j The phases of the phase windings after adjustment are j=1, 2, 3, 4, corresponding to θ 1 ,θ 2 ,θ 3 ,θ 4 ; Get θ 1 ,θ 2 ,θ 3 ,θ 4 The process is: When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back electromotive force of the four-phase windings B, C, D, and E is: In the formula, e B 、e C 、e D and e E are the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 and E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively; When an open-circuit fault occurs in the A-phase winding, the expression of the electromagnetic torque of the five-phase permanent magnet motor is: Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4 They are the average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor respectively; In order to improve the torque output characteristics of the five-phase permanent magnet motor after a one-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, while constraining the secondary fluctuation torque term to zero. The corresponding constraint condition expression is: Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows: Then, the phase of the adjusted B, C, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 2 ,θ 3 ,θ 4 .

2. Open-circuit fault-tolerant current setting method for five-phase permanent magnet motor considering the third harmonic of back EMF, It is characterized in that The method includes a fault-tolerant control method for open circuit of two-phase windings A and B: When the A and B two-phase windings are open circuited, adjust the input current of the remaining C, D, and E three-phase windings according to Work is performed to improve post-fault torque characteristics; In the formula, i C1 、i D1 、i E1 are the adjusted C, D, and E phase winding currents, I m1 is the amplitude of the adjusted C, D, and E phase winding current, ω is the current angular frequency, θ 2 ,θ 3 ,θ 4 are the phases of the adjusted C, D, and E phase winding currents respectively; By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 2 ,θ 3 ,θ 4 : In the formula, E 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively; λ 1 and λ 2 is the Lagrangian operator, θ j The phases of the phase winding current after adjustment j = 2, 3, 4, corresponding to θ 2 ,θ 3 ,θ 4 ; Get θ 2 ,θ 3 ,θ 4 The process is: When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the C, D, and E three-phase windings is: In the formula, e C 、e D and e E are the no-load back EMF of the four-phase windings B, C, D, and E, respectively. 1 、E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively; When an open circuit fault occurs in the A and B phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is: Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4 Five-phase permanent magnet The average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the motor; In order to improve the torque output characteristics of the five-phase permanent magnet motor after the adjacent two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, and at the same time constrain the secondary fluctuation torque term to zero. The corresponding constraint condition expression is: Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows: Then, the phase of the adjusted C, D, and E phase winding currents can be obtained, that is, θ 2 ,θ 3 ,θ 4 .

3. A method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor considering the third harmonic of back-EMF. It is characterized in that The method includes a fault-tolerant control method for open circuit of two-phase windings A and C: When the A and C phase windings are open circuit, adjust the input current of the remaining B, D, and E phase windings according to Work is performed to improve post-fault torque characteristics; In the formula, i B1 、i D1 、i E1 are the adjusted B, D, and E phase winding currents, I m1 is the amplitude of the B, D, and E phase winding current after adjustment, ω is the current angular frequency, θ 1 ,θ 3 ,θ 4 are the phases of the adjusted B, D, and E phase winding currents respectively; By considering the influence of the third harmonic of the back EMF and obtaining the corresponding objective function P based on the Lagrange multiplier method, θ is obtained. 1 ,θ 3 ,θ 4 : In the formula, E 1 and E 3 are the fundamental and third harmonic amplitudes of the no-load back EMF respectively; λ 1 and λ 2 is the Lagrangian operator, θ j is the adjusted phase winding current phase j = 1, 3, 4, corresponding to θ 1 ,θ 3 ,θ 4 ; Get θ 1 ,θ 3 ,θ 4 The process is: When the third harmonic in the rotor magnetic field is considered, the expression of the no-load back EMF of the three-phase windings B, D, and E is: In the formula, e B 、e D and e E are the no-load back EMF of the three-phase windings B, D, and E, respectively. 1 and E 3 are the amplitudes of the fundamental wave and third harmonic of the no-load back EMF respectively; When an open circuit fault occurs in the A and C phase windings, the expression of the electromagnetic torque of the five-phase permanent magnet motor is: Where, T em is the electromagnetic torque, Ω is the mechanical angular velocity of the motor rotor, T 0 , T 2 and T 4 They are the average torque term, the second-order ripple torque term and the fourth-order ripple torque term in the electromagnetic torque of the five-phase permanent magnet motor respectively; In order to improve the torque output characteristics of the five-phase permanent magnet motor after a two-phase winding open circuit fault, it is necessary to make the average torque term in the electromagnetic torque as large as possible, while constraining the secondary fluctuation torque term to zero. The corresponding constraint condition expression is: Based on the Lagrange multiplier method, the expression of the corresponding objective function P is obtained as follows: Then, the phase of the adjusted B, D, and E phase winding currents can be obtained, that is, θ 1 ,θ 3 ,θ 4 .

4. The method for setting the open-circuit fault-tolerant current of a five-phase permanent magnet motor considering the third harmonic of back-EMF according to claim 1, 2 or 3, It is characterized in that The five-phase permanent magnet motor is powered by a five-phase full-bridge inverter, a five-phase six-bridge-arm inverter or other five-phase multi-bridge-arm inverters that allow the neutral point current to be non-zero.

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